Question

Determine the matrix of the linear mapping $L$ with respect to the basis $B = \begin{Bmatrix} \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} -2 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} -2 \\ 0 \\ 2 \end{bmatrix} \end{Bmatrix}$, where \\ $[L(0, 1, 1)]_B = (3, 0, 0)$, $[L(-2, 1, 2)]_B = (0, 1, 0)$, $[L(-2, 0, 2)]_B = (0, 0, 0)$

          Determine the matrix of the linear mapping $L$ with respect to the basis $B = \begin{Bmatrix} \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} -2 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} -2 \\ 0 \\ 2 \end{bmatrix} \end{Bmatrix}$, where \\
$[L(0, 1, 1)]_B = (3, 0, 0)$, $[L(-2, 1, 2)]_B = (0, 1, 0)$, $[L(-2, 0, 2)]_B = (0, 0, 0)$

Determine the matrix of the linear mapping L with respect to the basis B =
< b m a t r i x >
,
< b m a t r i x >
,
< b m a t r i x >, where

[L(0, 1, 1)]B = (3, 0, 0), [L(-2, 1, 2)]B = (0, 1, 0), [L(-2, 0, 2)]B = (0, 0, 0)

Added by Shelia S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Jill Tolbert

Step 1

The image of the first basis vector i is given by [L0,1,1B=3,0,0]. Therefore, I(i) = 3i + 0j + 0k = [3, 0, 0]. The image of the second basis vector j is given by [L-2,1,2B=0,1,0]. Therefore, I(j) = 0i + 1j + 0k = [0, 1, 0]. The image of the third basis vector k Show more…

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